The Role of Self-Similarity in Fractal Photoconductive THz Emitters

2011 ◽  
Vol 32 (11) ◽  
pp. 1285-1290 ◽  
Author(s):  
Pouya Maraghechi ◽  
Abdulhakem Y. Elezzabi
Keyword(s):  
Self Similarity

Beckett's Broken Circle: A Literary Fractal

2020 ◽  
Vol 29 (2) ◽  
pp. 196-215
Author(s):  
Luke Connolly
Keyword(s):  
Dynamic Chaos ◽  
Geometric Form ◽  
Self Similarity ◽  
Collision Point ◽  
Stable Order ◽  
Structural Principle ◽  
Recent Interest ◽  
Viable Solution ◽  
Specific Shape

This essay proposes that the picture of a broken circle encountered by Watt during the second part of his tale marks a crucial collision point between Beckett's literary and mathematical interests and triggers a process of fractal scaling self-similarity. Building on recent interest concerning the role of the mathematics and mathematical forms found in Beckett's work, I argue that the broken circle depicted in the picture from Watt is a geometric form which (re)appears within at least three interlocking scales throughout Beckett's novel-length prose: (i) its moment of arrival in the picture from Watt, (ii) a macroscopic reinscription in the names of the protagonists populating the five novels spanning Watt through to The Unnamable and (iii) buried within the narratological depths of How It Is. As a structural principle, the interminable irregularity of fractals offered Beckett a viable solution for what he considered the defining task of the modern artist: ‘to find a form to accommodate the mess’. Moreover, the specific shape selected for his fractal is shown to contain within its geometry one of Beckett's most universal and pressing concerns: the inevitable insufficiency of language. Therefore, although this essay restricts itself to examining Beckett's novel-length prose, the idea of a broken circle fractal promises to provide a valuable heuristic through which to reassess the author's other generic avenues. Fractals thus offer a means through which one can bind together the length and breadth of Beckett's oeuvre without ever reducing dynamic chaos to stable order.

scholarly journals Topographic Analysis of Wetlandscapes: Fractal Dimension and Scaling Properties

10.29007/c7r5 ◽  
2018 ◽  
Author(s):  
Leonardo Enrico Bertassello ◽  
P. Suresh Rao ◽  
Gianluca Botter ◽  
Antoine Aubeneau
Keyword(s):  
Fractal Dimension ◽  
The United States ◽  
Self Similarity ◽  
Topographic Analysis ◽  
Scaling Properties ◽  
Dem Analysis ◽  
Water Filling ◽  
Topographic Depressions ◽  
And Storage

Wetlands are ubiquitous topographic depressions on landscapes and form criticalelements of the mosaic of aquatic habitats. The role of wetlands in the global hydrological and biogeochemical cycles is intimately tied to their geometric characteristics. We used DEM analysis and local search algorithms to identify wetland attributes (maximum stage, surface area and storage volume) in four wetlandscapes across the United States. We then derived the exceedance cumulative density functions (cdfs) of these attributes for the identified wetlands, applied the concept of fractal dimension to investigate the variability in wetland’ shapes. Exponentially tempered Pareto distributions were fitted to DEM derived wetland attributes. In particular, the scaling exponents appear to remain constant through the progressive water-filling of the landscapes, suggesting self-similarity of wetland geometrical attributes. This tendency is also reproduced by the fractal dimension (D) of wetland shorelines, which remains constant across different water-filling levels. In addition, the variability in D is constrained within a narrow range (1 <D < 1.33) in all the four wetlandscapes. Finally, the comparison between wetlands identified by the DEM-based model are consistentwith actual data.

scholarly journals Magnetic collimation of relativistic jets: the role of the black hole spin

2010 ◽  
Vol 6 (S274) ◽  
pp. 246-248
Author(s):  
N. Globus ◽  
C. Sauty ◽  
V. Cayatte
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Polar Axis ◽  
Kerr Metric ◽  
Relativistic Jets ◽  
Self Similarity ◽  
Simple Criterion ◽  
Frame Dragging ◽  
Grmhd Equations

AbstractAn ideal engine for producing ultrarelativistic jets is a rapidly rotating black hole threaded by a magnetic field. Following the 3+1 decomposion of spacetime of Thorne et al. (1986), we use a local inertial frame of reference attached to an observer comoving with the frame-dragging of the Kerr black hole (ZAMO) to write the GRMHD equations. Assuming θ-self similarity, analytical solutions for jets can be found for which the streamline shape is calculated exactly. Calculating the total energy variation between a non polar streamline and the polar axis, we have extended to the Kerr metric the simple criterion for the magnetic collimation of jets developed by Sauty et al. (1999). We show that the black hole rotation induces a more efficient magnetic collimation of the jet.

scholarly journals Generalized Finite-Length Fibonacci Sequences in Healthy and Pathological Human Walking: Comprehensively Assessing Recursivity, Asymmetry, Consistency, Self-Similarity, and Variability of Gaits

2021 ◽  
Vol 15 ◽  
Author(s):  
Cristiano Maria Verrelli ◽  
Marco Iosa ◽  
Paolo Roselli ◽  
Antonio Pisani ◽  
Franco Giannini ◽  
...  
Keyword(s):  
Finite Length ◽  
Golden Ratio ◽  
Point Of View ◽  
Human Walking ◽  
General Definition ◽  
Self Similarity ◽  
Time Intervals ◽  
Double Support ◽  
Fibonacci Sequences

Healthy and pathological human walking are here interpreted, from a temporal point of view, by means of dynamics-on-graph concepts and generalized finite-length Fibonacci sequences. Such sequences, in their most general definition, concern two sets of eight specific time intervals for the newly defined composite gait cycle, which involves two specific couples of overlapping (left and right) gait cycles. The role of the golden ratio, whose occurrence has been experimentally found in the recent literature, is accordingly characterized, without resorting to complex tools from linear algebra. Gait recursivity, self-similarity, and asymmetry (including double support sub-phase consistency) are comprehensively captured. A new gait index, named Φ-bonacci gait number, and a new related experimental conjecture—concerning the position of the foot relative to the tibia—are concurrently proposed. Experimental results on healthy or pathological gaits support the theoretical derivations.

scholarly journals Optimized Factor Approximants and Critical Index

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 903
Author(s):  
Simon Gluzman
Keyword(s):  
Effective Viscosity ◽  
Critical Index ◽  
Self Similarity ◽  
Critical Amplitude ◽  
Third Order ◽  
Symmetry Properties ◽  
Self Consistent ◽  
Minimal Difference ◽  
Order Coefficient

Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

scholarly journals Region-specific complexity of the intracranial EEG in the sleeping human brain

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Elzbieta Olejarczyk ◽  
Jean Gotman ◽  
Birgit Frauscher
Keyword(s):  
Sleep Stage ◽  
Brain Regions ◽  
Sleep Stages ◽  
Precentral Gyrus ◽  
Self Similarity ◽  
Intracranial Eeg ◽  
Brain Signals ◽  
Cortical Regions ◽  
The Brain

AbstractAs the brain is a complex system with occurrence of self-similarity at different levels, a dedicated analysis of the complexity of brain signals is of interest to elucidate the functional role of various brain regions across the various stages of vigilance. We exploited intracranial electroencephalogram data from 38 cortical regions using the Higuchi fractal dimension (HFD) as measure to assess brain complexity, on a dataset of 1772 electrode locations. HFD values depended on sleep stage and topography. HFD increased with higher levels of vigilance, being highest during wakefulness in the frontal lobe. HFD did not change from wake to stage N2 in temporo-occipital regions. The transverse temporal gyrus was the only area in which the HFD did not differ between any two vigilance stages. Interestingly, HFD of wakefulness and stage R were different mainly in the precentral gyrus, possibly reflecting motor inhibition in stage R. The fusiform and parahippocampal gyri were the only areas showing no difference between wakefulness and N2. Stages R and N2 were similar only for the postcentral gyrus. Topographical analysis of brain complexity revealed that sleep stages are clearly differentiated in fronto-central brain regions, but that temporo-occipital regions sleep differently.

The Role of Genes and Environment in Degree of Partner Self-Similarity

2016 ◽  
Vol 47 (1) ◽  
pp. 25-35 ◽  
Author(s):  
James M. Sherlock ◽  
Karin J. H. Verweij ◽  
Sean C. Murphy ◽  
Andrew C. Heath ◽  
Nicholas G. Martin ◽  
...  
Keyword(s):  
Self Similarity ◽  
Genes And Environment

scholarly journals STYLES OF BUSINESS COMMUNICATION AS A MODEL: THE PHENOMENON OF STYLE, APPROACHES, RESEARCH, OPEN QUESTIONS. PART 1

2019 ◽  
pp. 219-229
Author(s):  
Vladimir A. Tolochek ◽  
Keyword(s):  
Research And Development ◽  
Business Communication ◽  
Communication Styles ◽  
Research Subject ◽  
Development Programs ◽  
Self Similarity ◽  
Open Questions ◽  
Psychological System ◽  
Individual Style

Research into styles in psychology (from the 1950s to the 2000s) has undergone a kind of life cycle − from styles being widely studied to those falling into oblivion. Further constructive study of this problem requires creation of new R&D (research and development) programs, generalization of the experience gained in various schools of thought. The paper aims to provide a historical and theoretical analysis concerning the results of research on the phenomenon of «style» in Russian psychology; the research subject is the phenomenon of style (individual style of activity, styles of activity, styles of business communication). Hypotheses: 1. Regular reproduction of the same standard approaches in research and development does not promote constructive progress in the study of a scientific problem. 2. The study of the phenomenon of «style» based on the model of business communication styles allows us to emphasize several aspects in the evolution and functioning of style that were not distinguished when studying styles on other models (educational, sports, work). The article critically analyzes the history and results of studying the problem of style (individual style of activity, styles of activity) in Russian psychology (particularly within the Perm school), the use of the concept of «system» in Russian psychology, attitudes towards scientific opponents, trends in R & D within one school of thought, etc. The conditions for further constructive studies of the phenomenon of style are discussed (using new models that contribute to the discovery of new properties of style, making it possible not to attribute but to study its systemic properties as a unique psychological system; raising questions about the place and role of different styles in the processes of a phenomenon’s formation–development–functioning– disintegration, about the unity and difference of styles in the «chain» of their manifestations, about their structural and functional unity, about the self-similarity of their organization, etc.). Use of the model of business communication styles is believed to contribute to solving relevant scientific problems.

scholarly journals Momentum fractions carried by quarks and gluons in models of proton structure functions at small x

2017 ◽  
Vol 32 (18) ◽  
pp. 1750107 ◽  
Author(s):  
D. K. Choudhury ◽  
Baishali Saikia ◽  
K. Kalita
Keyword(s):  
Phenomenological Models ◽  
The Self ◽  
Proton Structure Function ◽  
Self Similarity ◽  
Proton Structure ◽  
Second Moments ◽  
Linear Rise ◽  
Small X ◽  
Comprehensive Comparison

In this paper, we report an analysis of partial momentum fractions carried by quarks and gluons in six alternative phenomenological models of proton structure function valid in limited small [Formula: see text] regions: [Formula: see text], [Formula: see text] to 6; the limits being determined by phenomenological range of validity in each model. Since the physics of small [Formula: see text] is not completely understood at this point, we have considered both self-similarity-based as well as QCD-based models. The procedure by which one can determine the applicability ranges in [Formula: see text] and [Formula: see text] of the models is presented. We find that while the self-similarity-based models with linear rise in [Formula: see text] has limited phenomenological ranges of validity, an improved version with linear rise in [Formula: see text] has a wider phenomenological range. We then compare the partial momentum fractions in all the small [Formula: see text] models. Our analysis implies that the role of small [Formula: see text] sea quarks in calculating the second moments of parton distribution is minor one. We have also made a comprehensive comparison of all the phenomenological models considered to the available perturbative QCD, lattice QCD as well as Ads/QCD results.

Bostwick Degree and Rheological Properties: an Up-to-date Viewpoint

2005 ◽  
Vol 15 (4) ◽  
pp. 218-229 ◽  
Author(s):  
Paolo Perona
Keyword(s):  
Rheological Properties ◽  
Yield Stress ◽  
Dynamic Behaviour ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Dimensionless Time ◽  
Self Similarity ◽  
Asymptotic Dynamic ◽  
Key Parameter

Abstract The correlation between the Bostwick degree and the static rheological properties of yield stress food fuids is first revisited and then reformulated in this work. The role of the yield stress in the free surface flow of the Bost-wick test is studied using dimensional analysis. Results from experiments on 48 different samples of yield stress fluids are considered and included to check the adequacy of the proposed correlation. Asymptotic dynamic behaviour is also presented and discussed as a mechanism of complete self similarity with respect of the dimensionless time. This approach would seem to support the opinions in favor of the yield stress as a key parameter, and thus offers an interesting new viewpoint useful to both future experiments on the Bostwick test and studies of 'dam-break' like dynamics.

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